Simplified Forms of the Transition Probabilities of the Two-Species ASEP with Some Initial Orders of Particles

Abstract

It has been known that the transition probability of the single species ASEP with $N$ particles is expressed as a sum of $N!$ $N$-fold contour integrals which are related to permutations in the symmetric group $S_N$. On other hand, the transition probabilities of the multi-species ASEP, in general, may be expressed as a sum of much more terms than $N!$. In this paper, we show that if the initial order of species is given by $2\cdots 21$, $12\cdots 2$, $1\cdots 12$ or $21\cdots 1$, then the transition probabilities can be expressed as a sum of at most $N!$ contour integrals, and provide their formulas explicitly.

References in corpus (6)

• On the asymmetric simple exclusion process with multiple species
• Determinant representation for some transition probabilities in the TASEP with second class particles
• Exact Formulas of the Transition Probabilities of the Multi-Species Asymmetric Simple Exclusion Process
• Coloured stochastic vertex models and their spectral theory
• On the TASEP with Second Class Particles
• Determinantal Expressions in Multi-Species TASEP